Where are the regulatory genes located in an operon?

What are promoter,operator,and structural genes?

An $E. coli$ cell with a mutated $z$ gene of the $lac$ operon cannot grow in a medium containing only lactose as the source of energy because:

$A$ low level of expression of lac operon occurs at all the time. Can you explain the logic behind this phenomenon?

An organism is able to survive on a culture medium containing nutrient $A$ through an enzyme-catalyzed process: $A \xrightarrow{X} B \xrightarrow{Y} C$. $A$ mutant organism fails to survive on this medium. However,it grows when nutrient $B$ is added to the medium. Which gene of this mutant is defective?

In prokaryotic $DNA$,the recognition of the promoter region by $RNA$ polymerase is determined in some cases by the interaction of certain proteins with which sequences?